Best Known (97, 123, s)-Nets in Base 4
(97, 123, 1045)-Net over F4 — Constructive and digital
Digital (97, 123, 1045)-net over F4, using
- 41 times duplication [i] based on digital (96, 122, 1045)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (78, 104, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 26, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 26, 257)-net over F256, using
- digital (5, 18, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(97, 123, 3737)-Net over F4 — Digital
Digital (97, 123, 3737)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4123, 3737, F4, 26) (dual of [3737, 3614, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4123, 4128, F4, 26) (dual of [4128, 4005, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4122, 4127, F4, 26) (dual of [4127, 4005, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 31, F4, 4) (dual of [31, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4122, 4127, F4, 26) (dual of [4127, 4005, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4123, 4128, F4, 26) (dual of [4128, 4005, 27]-code), using
(97, 123, 939061)-Net in Base 4 — Upper bound on s
There is no (97, 123, 939062)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 113 079424 244212 126682 572726 043354 952494 996488 483883 900849 961896 930452 643914 > 4123 [i]